02314_02341_03214_03241_03421_30214_30241_30421
Counting sequence:
1, 1, 2, 6, 24, 112, 562, 2918, 15403, 81970, 437954, 2344231, 12557040, 67272371, 360346709, 1929649625, 10329694293, 55277055634, 295705010060, 1581400308694, 8454915181416, 45193513349282, 241522003754139, 1290518212256267, 6894615687395056, 36830250830898821, 196723746050344601, 1050688360790247400, 5611286842633291706, 29965933449296541746, 160020066662270466230, 854488316189165486210, 4562742529221687084660, 24363322260528302099794, 130088789098569096993687, 694604770862955310439579, 3708784289056898285212704, 19802609950411875507847513, 105733166832923449255215563, 564545191893118866846210825, 3014292683051970532437379009, 16094289262788195969867056108, 85932650119280019771056021478, 458822691488908020282510581796, 2449807980724635276340566010776, 13080363617878030275104256089651, 69840654722532747472229293767591, 372904448648614142847949143190823, 1991075102450041109063312865325906, 10631108504075265260924966464701980, 56763647182014352967566359471065077, 303083890993943196022228754499280104, 1618289500220010348212451433067744771, 8640728344492225950100406874853653829, 46136561928142753279647323286056001442, 246343331699449968094614642650324398809, 1315337080410548833413875309190069938468, 7023182412152387061696375667494668150324, 37500013879252723690243616586111028629918, 200230147167441597708883725097660709358774, 1069123871736981124523142485634847591489281, 5708566625755749328928385667093845769692688, 30480815033298991614804684218396727105651169, 162752061793772256543159224062227290961010594, 869014083160225883863750515119882408308345568, 4640101641289385747080216291691990616845242914, 24775846976009164974904108518525551054776839434, 132290859474718066081251700998742666718200655711, 706368712278875804197686377968755088508323452094, 3771666961404435208100875889805253021670121966670, 20138887080743020776018559703718591412714863772937, 107532024783028638626498073325826997326367801728447, 574169858227837175486758827312709621401460145215798, 3065795270561478937225868471927758949234912538687902, 16369902336506918810131085651459595239029877008616609, 87407599135545787016903599942432309240068638759234810, 466715738303045124302166067633870628916704226190732748, 2492044772352148710252820695062657474450485159234135202, 13306362909213254589434537419655264011023883239631259569, 71049823911805544930640391180103864495462868989122836837, 379373295560625807538912747803892297951871056155255557491, 2025678922774512888552417721198258506143168724378976860863, 10816196139555846002257025598054204680355416990891149225809, 57753536673743199022694802570235892856334785075600614356807, 308377507217955146203773400334730596286807011103171325335474, 1646595313797125155769110047311530477552414192294340115182049, 8792069723534865281068163511107844579761885617118360039203740, 46945658313648894712795227606119651250653163684596436723316197, 250668521938005489401023623481179997093027937389358581075608212, 1338456370836892499131122188835313298217742598470077840120977460, 7146751580392121644304955887344093559444907842436936278395463467, 38160424564365283177644303256507171502025245678415333044674032668, 203759445633369892326193448746765419209592464311178381546174472937, 1087983578887733401377783125002405585222479708384324852276371832908, 5809342280959278604839029521030580692802461201938994784801635841668, 31019273527826924783191575658365598494532317707582013933613371235523, 165628972973475193534136497027583596731975043395836933592669688411129, 884384296890132390371536789899625490116975775580931755172192834308782, 4722215055647271567124118441167433492494360473761540128158233867051304, 25214509461331457640404127713845822296526794997657202536385415052922006, 134634172981888153496638510375421293600956095854182302583052189803074365
Implicit equation for the generating function in Maple syntax:
(81*x^22-540*x^21+5454*x^20-23316*x^19+105880*x^18-309463*x^17+735212*x^16-1335670*x^15+1530326*x^14-1493583*x^13+3049706*x^12-6766688*x^11+9919499*x^10-9722923*x^9+6690919*x^8-3328348*x^7+1211881*x^6-322925*x^5+62202*x^4-8423*x^3+760*x^2-41*x+1)*F(x)^4+(324*x^21-1566*x^20+14886*x^19-57834*x^18+238026*x^17-698796*x^16+1707853*x^15-3794676*x^14+7134154*x^13-11878642*x^12+18112712*x^11-23289690*x^10+23120582*x^9-17029705*x^8+9193469*x^7-3621970*x^6+1035154*x^5-211750*x^4+30172*x^3-2842*x^2+159*x-4)*F(x)^3+(396*x^20-1320*x^19+12311*x^18-39274*x^17+171519*x^16-543564*x^15+1557326*x^14-3842021*x^13+7419779*x^12-11807747*x^11+15992004*x^10-17580157*x^9+14682018*x^8-8944843*x^7+3911106*x^6-1217988*x^5+267137*x^4-40281*x^3+3974*x^2-231*x+6)*F(x)^2+(4*x^2-6*x+1)*(36*x^10-54*x^9+462*x^8-1560*x^7+2910*x^6-4441*x^5+4323*x^4-2203*x^3+584*x^2-77*x+4)*(x^7+12*x^5+9*x^4+57*x^3-47*x^2+12*x-1)*F(x)+(4*x^2-6*x+1)^2*(x^7+12*x^5+9*x^4+57*x^3-47*x^2+12*x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
\left(81 x^{22}-540 x^{21}+5454 x^{20}-23316 x^{19}+105880 x^{18}-309463 x^{17}+735212 x^{16}-1335670 x^{15}+1530326 x^{14}-1493583 x^{13}+3049706 x^{12}-6766688 x^{11}+9919499 x^{10}-9722923 x^{9}+6690919 x^{8}-3328348 x^{7}+1211881 x^{6}-322925 x^{5}+62202 x^{4}-8423 x^{3}+760 x^{2}-41 x +1\right) F \! \left(x \right)^{4}+\left(324 x^{21}-1566 x^{20}+14886 x^{19}-57834 x^{18}+238026 x^{17}-698796 x^{16}+1707853 x^{15}-3794676 x^{14}+7134154 x^{13}-11878642 x^{12}+18112712 x^{11}-23289690 x^{10}+23120582 x^{9}-17029705 x^{8}+9193469 x^{7}-3621970 x^{6}+1035154 x^{5}-211750 x^{4}+30172 x^{3}-2842 x^{2}+159 x -4\right) F \! \left(x \right)^{3}+\left(396 x^{20}-1320 x^{19}+12311 x^{18}-39274 x^{17}+171519 x^{16}-543564 x^{15}+1557326 x^{14}-3842021 x^{13}+7419779 x^{12}-11807747 x^{11}+15992004 x^{10}-17580157 x^{9}+14682018 x^{8}-8944843 x^{7}+3911106 x^{6}-1217988 x^{5}+267137 x^{4}-40281 x^{3}+3974 x^{2}-231 x +6\right) F \! \left(x \right)^{2}+\left(4 x^{2}-6 x +1\right) \left(36 x^{10}-54 x^{9}+462 x^{8}-1560 x^{7}+2910 x^{6}-4441 x^{5}+4323 x^{4}-2203 x^{3}+584 x^{2}-77 x +4\right) \left(x^{7}+12 x^{5}+9 x^{4}+57 x^{3}-47 x^{2}+12 x -1\right) F \! \left(x \right)+\left(4 x^{2}-6 x +1\right)^{2} \left(x^{7}+12 x^{5}+9 x^{4}+57 x^{3}-47 x^{2}+12 x -1\right)^{2} = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 112
a(6) = 562
a(7) = 2918
a(8) = 15403
a(9) = 81970
a(10) = 437954
a(11) = 2344231
a(12) = 12557040
a(13) = 67272371
a(14) = 360346709
a(15) = 1929649625
a(16) = 10329694293
a(17) = 55277055634
a(18) = 295705010060
a(19) = 1581400308694
a(20) = 8454915181416
a(21) = 45193513349282
a(22) = 241522003754139
a(23) = 1290518212256267
a(24) = 6894615687395056
a(25) = 36830250830898821
a(26) = 196723746050344601
a(27) = 1050688360790247400
a(28) = 5611286842633291706
a(29) = 29965933449296541746
a(30) = 160020066662270466230
a(31) = 854488316189165486210
a(32) = 4562742529221687084660
a(33) = 24363322260528302099794
a(34) = 130088789098569096993687
a(35) = 694604770862955310439579
a(36) = 3708784289056898285212704
a(37) = 19802609950411875507847513
a(38) = 105733166832923449255215563
a(39) = 564545191893118866846210825
a(40) = 3014292683051970532437379009
a(41) = 16094289262788195969867056108
a(42) = 85932650119280019771056021478
a(43) = 458822691488908020282510581796
a(44) = 2449807980724635276340566010776
a(45) = 13080363617878030275104256089651
a(46) = 69840654722532747472229293767591
a(47) = 372904448648614142847949143190823
a(48) = 1991075102450041109063312865325906
a(49) = 10631108504075265260924966464701980
a(50) = 56763647182014352967566359471065077
a(51) = 303083890993943196022228754499280104
a(52) = 1618289500220010348212451433067744771
a(53) = 8640728344492225950100406874853653829
a(54) = 46136561928142753279647323286056001442
a(55) = 246343331699449968094614642650324398809
a(56) = 1315337080410548833413875309190069938468
a(57) = 7023182412152387061696375667494668150324
a(58) = 37500013879252723690243616586111028629918
a(59) = 200230147167441597708883725097660709358774
a(60) = 1069123871736981124523142485634847591489281
a(61) = 5708566625755749328928385667093845769692688
a(62) = 30480815033298991614804684218396727105651169
a(63) = 162752061793772256543159224062227290961010594
a(64) = 869014083160225883863750515119882408308345568
a(65) = 4640101641289385747080216291691990616845242914
a(66) = 24775846976009164974904108518525551054776839434
a(67) = 132290859474718066081251700998742666718200655711
a(68) = 706368712278875804197686377968755088508323452094
a(69) = 3771666961404435208100875889805253021670121966670
a(70) = 20138887080743020776018559703718591412714863772937
a(71) = 107532024783028638626498073325826997326367801728447
a(72) = 574169858227837175486758827312709621401460145215798
a(73) = 3065795270561478937225868471927758949234912538687902
a(74) = 16369902336506918810131085651459595239029877008616609
a(75) = 87407599135545787016903599942432309240068638759234810
a(76) = 466715738303045124302166067633870628916704226190732748
a(77) = 2492044772352148710252820695062657474450485159234135202
a(78) = 13306362909213254589434537419655264011023883239631259569
a(79) = 71049823911805544930640391180103864495462868989122836837
a(80) = 379373295560625807538912747803892297951871056155255557491
a(81) = 2025678922774512888552417721198258506143168724378976860863
a(n+82) = -1/12*(263739959886277599197756460383*n^3+42138201095852442920367796668594*n^2+2243958594696662432099854608398857*n+39828354753999535428684329853640518)/(n+80)/(n+79)/(n+81)*a(n+54)+1/12*(108880017037838702319257591251*n^3+17680251003971652554340466308660*n^2+956936190769700265399536282613551*n+17263605623691015102097290386732826)/(n+80)/(n+79)/(n+81)*a(n+55)+1/4*(740701369086677635681*n^3+145356602934499151024830*n^2+9508252101639787122511905*n+207319954451921018041500952)/(n+80)/(n+79)/(n+81)*a(n+67)+1/12*(104156065366802972993395*n^3+19836842684493587530482186*n^2+1259322239147613665036913989*n+26648802165587938753968266670)/(n+80)/(n+79)/(n+81)*a(n+65)-1/12*(15945477311703672921901*n^3+3082964105939327297382696*n^2+198689437379131091776767857*n+4268316684242164573923104994)/(n+80)/(n+79)/(n+81)*a(n+66)+1/4*(734779451951671158462502711*n^3+38943566039311203606629748688*n^2+684571701262092416051473190213*n+3991842464067579121380976005788)/(n+80)/(n+79)/(n+81)*a(n+17)-1/6*(20386015717506941494195943893*n^3+3364911010609884252329570916114*n^2+185130899517271376133090009151946*n+3395064018388268246585527273566303)/(n+80)/(n+79)/(n+81)*a(n+56)-1/6*(140545053617753151529*n^3+27988868364901703801475*n^2+1857925515512158289635847*n+41109731189386669396400397)/(n+80)/(n+79)/(n+81)*a(n+68)+1/6*(16082640696857042936*n^3+3249547543572391119861*n^2+218857007733428329155859*n+4913265560257858615875228)/(n+80)/(n+79)/(n+81)*a(n+69)-78732*(3572158890086*n^3+66022916313492*n^2+402763496282311*n+809446830490717)/(n+80)/(n+79)/(n+81)*a(n+4)-1/12*(55396553929878968116975389186283*n^3+5821429037467354126693628757427830*n^2+202749975263373010050086322325962557*n+2337927639429702219452304518353140234)/(n+80)/(n+79)/(n+81)*a(n+38)+1/4*(4634720109473806034009340901*n^3+777635939857731159218565892246*n^2+43491005947589960965171417896549*n+810760481516315944253432866354856)/(n+80)/(n+79)/(n+81)*a(n+57)-9*(3105460762345048096476*n^3+107425290240246956092364*n^2+1234597183807518144050463*n+4716330251836149026957269)/(n+80)/(n+79)/(n+81)*a(n+10)-81/2*(24003721055122305863*n^3+700513428477108895536*n^2+6793577454604954484683*n+21899394540950772170838)/(n+80)/(n+79)/(n+81)*a(n+8)-(14457*n^2+2243175*n+87011284)/(n+81)/(n+80)*a(n+80)-1/12*(1124676906340852409846799017897*n^3+174193739140460769367156501937538*n^2+8990994243250990699702607823865597*n+154651969115579282403641848955789424)/(n+80)/(n+79)/(n+81)*a(n+52)+1/6*(25548027755358540863740353904*n^3+30632350149991244697236714896713*n^2+2668914162965541949521288492733541*n+60444034147871467449133358020088574)/(n+80)/(n+79)/(n+81)*a(n+47)+1/6*(5158158439589133572206235453060*n^3+552865493207060072519720946020883*n^2+19533564499241082189950123692375948*n+227901883063163517898258914578298957)/(n+80)/(n+79)/(n+81)*a(n+33)-1/6*(8425206547925639960304686*n^3+1531989138621588264003907176*n^2+92855805114143121518158178365*n+1876034065721753255186063899725)/(n+80)/(n+79)/(n+81)*a(n+62)+1/12*(3380692802466440215528679*n^3+624401825757223631081054922*n^2+38441512317498118428067445371*n+788886821991342958093660455084)/(n+80)/(n+79)/(n+81)*a(n+63)+1/2*(7741367317458531299878975848583*n^3+821185529243180148928440866234199*n^2+28825785349946662426546562419112258*n+334355610615725356648283281482586268)/(n+80)/(n+79)/(n+81)*a(n+39)+1/12*(3416547217004269004504632479853*n^3+514482569148370300845314230026894*n^2+25774717648103112599775764449670243*n+429660974370990175391551354490956746)/(n+80)/(n+79)/(n+81)*a(n+49)-1/4*(206901855787934610514557*n^3+38808583572105480146360440*n^2+2426433442679558433295029687*n+50569223718527858844069389820)/(n+80)/(n+79)/(n+81)*a(n+64)-1/6*(9128227277755756279617237446687*n^3+943664886752371318967427184696665*n^2+32343473439809817787236236153011318*n+367575849574598534736912347214920106)/(n+80)/(n+79)/(n+81)*a(n+34)+1/12*(55641816030447403110488949887*n^3+2824682219680220797548107746104*n^2+42299754201850901494502363630785*n+155925858945156047797507164749040)/(n+80)/(n+79)/(n+81)*a(n+23)+1/4*(9962228114858019857160096239137*n^3+1016244258621031413715236765457348*n^2+34399395964690573942483605872776831*n+386209068079626060782612349621732076)/(n+80)/(n+79)/(n+81)*a(n+35)-1/12*(2794640083020662502053649186467*n^3+431755443411702099328252376474412*n^2+22071850181903537786484656026532017*n+373779468381958109167671761649545928)/(n+80)/(n+79)/(n+81)*a(n+48)-1/3*(1323914521049525975575301776*n^3+73186552150323394064638042536*n^2+1341591440631128005949371084157*n+8154677872705460715500480538267)/(n+80)/(n+79)/(n+81)*a(n+18)+1/3*(1611969781643*n^3+353918345019147*n^2+25900851867996556*n+631815024704732976)/(n+80)/(n+79)/(n+81)*a(n+75)-(25269511240*n^3+5621905464315*n^2+416901841695509*n+10304994955090918)/(n+80)/(n+79)/(n+81)*a(n+76)+1/2*(1986202315*n^3+447688600924*n^2+33634962536591*n+842302941730078)/(n+80)/(n+79)/(n+81)*a(n+77)+729/2*(423471619613912009*n^3+11218255122821175242*n^2+98734275882971144935*n+288701635267882449918)/(n+80)/(n+79)/(n+81)*a(n+7)-1/12*(5790414274788357193953122437789*n^3+650315571601712340785094015226086*n^2+23769630851858662875606148196428397*n+284436629489472923024302278489334776)/(n+80)/(n+79)/(n+81)*a(n+32)+1/12*(576099749615410279337146938047*n^3+90594612252483662582073724070412*n^2+4748108285335752100024294496599489*n+82937882726481380501139933787332924)/(n+80)/(n+79)/(n+81)*a(n+53)+1/4*(1736558236533300322927778936161*n^3+213013909821337732816916685771250*n^2+8600846348512538661647652260779719*n+113919267840221666221089622060250374)/(n+80)/(n+79)/(n+81)*a(n+46)+1/12*(7655203900115914646474527406491*n^3+654035489295274408498844869645152*n^2+15718316580422951030720245013669291*n+72362110211188970718507473738396778)/(n+80)/(n+79)/(n+81)*a(n+41)-1/6*(222099592884156307950059573174*n^3+20849135186919303578297853084621*n^2+682317311976714212678342700552418*n+7639112562063703014322498000510599)/(n+80)/(n+79)/(n+81)*a(n+28)-(31726902*n^3+7243905916*n^2+551288672693*n+13984487375393)/(n+80)/(n+79)/(n+81)*a(n+78)+2/3*(1187096*n^3+274505910*n^2+21158138614*n+543579636477)/(n+80)/(n+79)/(n+81)*a(n+79)+1/6*(62104203543975898474319896889*n^3+3719492780362250122879717528473*n^2+88393315170398268641926708030654*n+901210099294825100116143382340700)/(n+80)/(n+79)/(n+81)*a(n+27)+1/4*(5808126714654278917915125500603*n^3+743464736330267891717474950225600*n^2+31658857924471665086864835774714353*n+448416642880604417814531031406814132)/(n+80)/(n+79)/(n+81)*a(n+44)-1/12*(4329844799808913868110813919*n^3+738441026828569960674599833680*n^2+41979137364502851011205672296905*n+795472472997659804535821680900536)/(n+80)/(n+79)/(n+81)*a(n+58)-1/3*(6302940342496109*n^3+1328638297636994214*n^2+93355255484997380668*n+2186449168780173946731)/(n+80)/(n+79)/(n+81)*a(n+72)+1/6*(917185180255633*n^3+196016613777963318*n^2+13963553697977370791*n+331563275516843451894)/(n+80)/(n+79)/(n+81)*a(n+73)-1/3*(29223716315678*n^3+6330894849532299*n^2+457152150806131234*n+11003290830134460909)/(n+80)/(n+79)/(n+81)*a(n+74)-1/12*(2853943166473652806517363765683*n^3+431230696563459072684233974707660*n^2+21701605218907632990464377294742711*n+363756435557815005946448375718922842)/(n+80)/(n+79)/(n+81)*a(n+50)+2/3*(6672265421074648937015529965183*n^3+691452982792260202804307258252835*n^2+23761407133590144956945899759295383*n+270533991558933880754631188503568964)/(n+80)/(n+79)/(n+81)*a(n+37)-1/12*(50224999938974819279694901351*n^3+2899796741655322453795052153982*n^2+54503587532967228937752645400535*n+330374964640632256759724303901300)/(n+80)/(n+79)/(n+81)*a(n+22)+1/4*(8374756678678072743086077*n^3+357601413327000483030912116*n^2+5068803701205756522322467695*n+23863190925514368143413185016)/(n+80)/(n+79)/(n+81)*a(n+13)+3/4*(172320641244373364058177*n^3+6427900477737497457871910*n^2+79638967277547020528580903*n+327906462338935536084226666)/(n+80)/(n+79)/(n+81)*a(n+11)-1/2*(1088825724912559699779695*n^3+43561120577709788213274603*n^2+578682958901617982545402732*n+2554058559230855735873047950)/(n+80)/(n+79)/(n+81)*a(n+12)+314928*(77698226146*n^3+1229843464776*n^2+6376844729861*n+10794223433496)/(n+80)/(n+79)/(n+81)*a(n+3)-729*(29812520893130381*n^3+709810630814935464*n^2+5610298385820787123*n+14714971309282940460)/(n+80)/(n+79)/(n+81)*a(n+6)+1/3*(2850804579972188471628361268*n^3+163282344025250614817641847658*n^2+3100098964418064054620681812003*n+19504315574431749151704487557165)/(n+80)/(n+79)/(n+81)*a(n+19)+1/2*(2896995017906206252299296130*n^3-343489994778188390924917055143*n^2-20842743707011922696952650931347*n-260690145701652966744289054216488)/(n+80)/(n+79)/(n+81)*a(n+25)+1/4*(350820338698897698578619858897*n^3+37204595640942033797343492272940*n^2+1304870181779514657111689704947421*n+15110842152671854703959737631749838)/(n+80)/(n+79)/(n+81)*a(n+29)-1/6*(993291518049651190499950185929*n^3+111981852967228710914183382420642*n^2+4083822626987204407858106477998510*n+48551268609525237187481960082564495)/(n+80)/(n+79)/(n+81)*a(n+30)+1/6*(967009329807494484788734098632*n^3+147716343814678957686242626654290*n^2+7518246302934403874135424145236409*n+127497305131387274479844691485160969)/(n+80)/(n+79)/(n+81)*a(n+51)+2*(86*n+6715)/(n+81)*a(n+81)-1/4*(14396147713283826139341161425*n^3+355164975376210731443618364690*n^2-6654773891720125216311131463489*n-164920939980837525701262372327562)/(n+80)/(n+79)/(n+81)*a(n+24)-1/12*(17522650379849377782719663197061*n^3+2264764790771331297643937623723170*n^2+97275816849931001827087852663488865*n+1388607116148799458356123286527404344)/(n+80)/(n+79)/(n+81)*a(n+43)+1/6*(4566248011347113045030597380118*n^3+640947300901917041387126645919594*n^2+29414368067877867570844245497059543*n+443178931271932239967645734580987041)/(n+80)/(n+79)/(n+81)*a(n+42)+1/12*(76926359920025582639517151*n^3+13768658574269269469839670664*n^2+821459867020179268024832526767*n+16336511580123956028896015744178)/(n+80)/(n+79)/(n+81)*a(n+61)-1/6*(8391059088562891240578067378*n^3-1438926022504876622086848190065*n^2-79588934278930067710500139000516*n-946673328685323797038307914260477)/(n+80)/(n+79)/(n+81)*a(n+26)+1/4*(94456153825423344641710723*n^3+4533152332521091948789834938*n^2+72183475896890119051617200977*n+381524382545652068862149920938)/(n+80)/(n+79)/(n+81)*a(n+15)-1/2*(138193245436656022167213333*n^3+6985598505188369822880949877*n^2+117139176940313957389931344814*n+651798837297291964928349738324)/(n+80)/(n+79)/(n+81)*a(n+16)-1/4*(7247222552349986565393207379*n^3+425907696296638003908617213370*n^2+8289247397838179760784439485765*n+53383602737263776282398741764870)/(n+80)/(n+79)/(n+81)*a(n+20)-403895160000*(2*n+7)*(2*n+5)*(n+1)/(n+80)/(n+79)/(n+81)*a(n)+141717600*(2*n+7)*(278826*n^2+1917250*n+2711881)/(n+80)/(n+79)/(n+81)*a(n+1)+1/12*(36014580661124589800962525421*n^3+2135505473337184537684202691972*n^2+41800562451407588407912604356201*n+269523761251906121417922519191622)/(n+80)/(n+79)/(n+81)*a(n+21)+27/2*(406370501146335770603*n^3+12957067872577567658914*n^2+137282081080186177152169*n+483528905098352738916794)/(n+80)/(n+79)/(n+81)*a(n+9)-4723920*(350576999*n^3+4625788994*n^2+19688856094*n+26861403394)/(n+80)/(n+79)/(n+81)*a(n+2)-2/3*(1498134425520806623942692242408*n^3+190754735142566953406515426586688*n^2+8070447366658427089220786269044286*n+113408099027823923158830429613727955)/(n+80)/(n+79)/(n+81)*a(n+45)-1/2*(14714783669242085262715217*n^3+667568756730896037050181368*n^2+10050897351579940025464746369*n+50245273212201573655825065410)/(n+80)/(n+79)/(n+81)*a(n+14)+1/6*(1693273282488146319054361021681*n^3+194742828021963580662532198872168*n^2+7214393056239009200394846531661292*n+86940661819627061422778664685429383)/(n+80)/(n+79)/(n+81)*a(n+31)+4374*(611192213987126*n^3+12920040947864502*n^2+90499559062078261*n+209846403202586607)/(n+80)/(n+79)/(n+81)*a(n+5)-(3593950091265193077871447568163*n^3+367964668396402170998734453211536*n^2+12497255759548666439219523279100059*n+140696367706211029942956523943056896)/(n+80)/(n+79)/(n+81)*a(n+36)+1/3*(308366033167335343024589591*n^3+53451423098225195843564006946*n^2+3088364396343971929791331665880*n+59480438361170695482401948905191)/(n+80)/(n+79)/(n+81)*a(n+59)-1/12*(321798990321296570989457245*n^3+56685439453304505247133811846*n^2+3328404740125417702521254681303*n+65144601432550636410983759760558)/(n+80)/(n+79)/(n+81)*a(n+60)-1/6*(14254592339082593726737572569348*n^3+1496069890184425565331595488533379*n^2+51626652634338957367898284147785346*n+583515182104364957842592016051354267)/(n+80)/(n+79)/(n+81)*a(n+40)-1/12*(3315695637812237203*n^3+679600927375054410828*n^2+46430580031866876999185*n+1057365867130436102517240)/(n+80)/(n+79)/(n+81)*a(n+70)+1/6*(153170758123592719*n^3+31841064070536420060*n^2+2206322152908481178261*n+50958906942255920965992)/(n+80)/(n+79)/(n+81)*a(n+71), n >= 82
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 112
a(6) = 562
a(7) = 2918
a(8) = 15403
a(9) = 81970
a(10) = 437954
a(11) = 2344231
a(12) = 12557040
a(13) = 67272371
a(14) = 360346709
a(15) = 1929649625
a(16) = 10329694293
a(17) = 55277055634
a(18) = 295705010060
a(19) = 1581400308694
a(20) = 8454915181416
a(21) = 45193513349282
a(22) = 241522003754139
a(23) = 1290518212256267
a(24) = 6894615687395056
a(25) = 36830250830898821
a(26) = 196723746050344601
a(27) = 1050688360790247400
a(28) = 5611286842633291706
a(29) = 29965933449296541746
a(30) = 160020066662270466230
a(31) = 854488316189165486210
a(32) = 4562742529221687084660
a(33) = 24363322260528302099794
a(34) = 130088789098569096993687
a(35) = 694604770862955310439579
a(36) = 3708784289056898285212704
a(37) = 19802609950411875507847513
a(38) = 105733166832923449255215563
a(39) = 564545191893118866846210825
a(40) = 3014292683051970532437379009
a(41) = 16094289262788195969867056108
a(42) = 85932650119280019771056021478
a(43) = 458822691488908020282510581796
a(44) = 2449807980724635276340566010776
a(45) = 13080363617878030275104256089651
a(46) = 69840654722532747472229293767591
a(47) = 372904448648614142847949143190823
a(48) = 1991075102450041109063312865325906
a(49) = 10631108504075265260924966464701980
a(50) = 56763647182014352967566359471065077
a(51) = 303083890993943196022228754499280104
a(52) = 1618289500220010348212451433067744771
a(53) = 8640728344492225950100406874853653829
a(54) = 46136561928142753279647323286056001442
a(55) = 246343331699449968094614642650324398809
a(56) = 1315337080410548833413875309190069938468
a(57) = 7023182412152387061696375667494668150324
a(58) = 37500013879252723690243616586111028629918
a(59) = 200230147167441597708883725097660709358774
a(60) = 1069123871736981124523142485634847591489281
a(61) = 5708566625755749328928385667093845769692688
a(62) = 30480815033298991614804684218396727105651169
a(63) = 162752061793772256543159224062227290961010594
a(64) = 869014083160225883863750515119882408308345568
a(65) = 4640101641289385747080216291691990616845242914
a(66) = 24775846976009164974904108518525551054776839434
a(67) = 132290859474718066081251700998742666718200655711
a(68) = 706368712278875804197686377968755088508323452094
a(69) = 3771666961404435208100875889805253021670121966670
a(70) = 20138887080743020776018559703718591412714863772937
a(71) = 107532024783028638626498073325826997326367801728447
a(72) = 574169858227837175486758827312709621401460145215798
a(73) = 3065795270561478937225868471927758949234912538687902
a(74) = 16369902336506918810131085651459595239029877008616609
a(75) = 87407599135545787016903599942432309240068638759234810
a(76) = 466715738303045124302166067633870628916704226190732748
a(77) = 2492044772352148710252820695062657474450485159234135202
a(78) = 13306362909213254589434537419655264011023883239631259569
a(79) = 71049823911805544930640391180103864495462868989122836837
a(80) = 379373295560625807538912747803892297951871056155255557491
a(81) = 2025678922774512888552417721198258506143168724378976860863
a{\left(n + 82 \right)} = - \frac{403895160000 \left(n + 1\right) \left(2 n + 5\right) \left(2 n + 7\right) a{\left(n \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{2 \left(86 n + 6715\right) a{\left(n + 81 \right)}}{n + 81} - \frac{\left(14457 n^{2} + 2243175 n + 87011284\right) a{\left(n + 80 \right)}}{\left(n + 80\right) \left(n + 81\right)} + \frac{141717600 \left(2 n + 7\right) \left(278826 n^{2} + 1917250 n + 2711881\right) a{\left(n + 1 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{2 \left(1187096 n^{3} + 274505910 n^{2} + 21158138614 n + 543579636477\right) a{\left(n + 79 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(31726902 n^{3} + 7243905916 n^{2} + 551288672693 n + 13984487375393\right) a{\left(n + 78 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{4723920 \left(350576999 n^{3} + 4625788994 n^{2} + 19688856094 n + 26861403394\right) a{\left(n + 2 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(1986202315 n^{3} + 447688600924 n^{2} + 33634962536591 n + 842302941730078\right) a{\left(n + 77 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(25269511240 n^{3} + 5621905464315 n^{2} + 416901841695509 n + 10304994955090918\right) a{\left(n + 76 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{314928 \left(77698226146 n^{3} + 1229843464776 n^{2} + 6376844729861 n + 10794223433496\right) a{\left(n + 3 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(1611969781643 n^{3} + 353918345019147 n^{2} + 25900851867996556 n + 631815024704732976\right) a{\left(n + 75 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{78732 \left(3572158890086 n^{3} + 66022916313492 n^{2} + 402763496282311 n + 809446830490717\right) a{\left(n + 4 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(29223716315678 n^{3} + 6330894849532299 n^{2} + 457152150806131234 n + 11003290830134460909\right) a{\left(n + 74 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{4374 \left(611192213987126 n^{3} + 12920040947864502 n^{2} + 90499559062078261 n + 209846403202586607\right) a{\left(n + 5 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(917185180255633 n^{3} + 196016613777963318 n^{2} + 13963553697977370791 n + 331563275516843451894\right) a{\left(n + 73 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(6302940342496109 n^{3} + 1328638297636994214 n^{2} + 93355255484997380668 n + 2186449168780173946731\right) a{\left(n + 72 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{729 \left(29812520893130381 n^{3} + 709810630814935464 n^{2} + 5610298385820787123 n + 14714971309282940460\right) a{\left(n + 6 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(153170758123592719 n^{3} + 31841064070536420060 n^{2} + 2206322152908481178261 n + 50958906942255920965992\right) a{\left(n + 71 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{729 \left(423471619613912009 n^{3} + 11218255122821175242 n^{2} + 98734275882971144935 n + 288701635267882449918\right) a{\left(n + 7 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(3315695637812237203 n^{3} + 679600927375054410828 n^{2} + 46430580031866876999185 n + 1057365867130436102517240\right) a{\left(n + 70 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(16082640696857042936 n^{3} + 3249547543572391119861 n^{2} + 218857007733428329155859 n + 4913265560257858615875228\right) a{\left(n + 69 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{81 \left(24003721055122305863 n^{3} + 700513428477108895536 n^{2} + 6793577454604954484683 n + 21899394540950772170838\right) a{\left(n + 8 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(140545053617753151529 n^{3} + 27988868364901703801475 n^{2} + 1857925515512158289635847 n + 41109731189386669396400397\right) a{\left(n + 68 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{27 \left(406370501146335770603 n^{3} + 12957067872577567658914 n^{2} + 137282081080186177152169 n + 483528905098352738916794\right) a{\left(n + 9 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(740701369086677635681 n^{3} + 145356602934499151024830 n^{2} + 9508252101639787122511905 n + 207319954451921018041500952\right) a{\left(n + 67 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{9 \left(3105460762345048096476 n^{3} + 107425290240246956092364 n^{2} + 1234597183807518144050463 n + 4716330251836149026957269\right) a{\left(n + 10 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(15945477311703672921901 n^{3} + 3082964105939327297382696 n^{2} + 198689437379131091776767857 n + 4268316684242164573923104994\right) a{\left(n + 66 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(104156065366802972993395 n^{3} + 19836842684493587530482186 n^{2} + 1259322239147613665036913989 n + 26648802165587938753968266670\right) a{\left(n + 65 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{3 \left(172320641244373364058177 n^{3} + 6427900477737497457871910 n^{2} + 79638967277547020528580903 n + 327906462338935536084226666\right) a{\left(n + 11 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(206901855787934610514557 n^{3} + 38808583572105480146360440 n^{2} + 2426433442679558433295029687 n + 50569223718527858844069389820\right) a{\left(n + 64 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(1088825724912559699779695 n^{3} + 43561120577709788213274603 n^{2} + 578682958901617982545402732 n + 2554058559230855735873047950\right) a{\left(n + 12 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(3380692802466440215528679 n^{3} + 624401825757223631081054922 n^{2} + 38441512317498118428067445371 n + 788886821991342958093660455084\right) a{\left(n + 63 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(8374756678678072743086077 n^{3} + 357601413327000483030912116 n^{2} + 5068803701205756522322467695 n + 23863190925514368143413185016\right) a{\left(n + 13 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(8425206547925639960304686 n^{3} + 1531989138621588264003907176 n^{2} + 92855805114143121518158178365 n + 1876034065721753255186063899725\right) a{\left(n + 62 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(14714783669242085262715217 n^{3} + 667568756730896037050181368 n^{2} + 10050897351579940025464746369 n + 50245273212201573655825065410\right) a{\left(n + 14 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(76926359920025582639517151 n^{3} + 13768658574269269469839670664 n^{2} + 821459867020179268024832526767 n + 16336511580123956028896015744178\right) a{\left(n + 61 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(94456153825423344641710723 n^{3} + 4533152332521091948789834938 n^{2} + 72183475896890119051617200977 n + 381524382545652068862149920938\right) a{\left(n + 15 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(138193245436656022167213333 n^{3} + 6985598505188369822880949877 n^{2} + 117139176940313957389931344814 n + 651798837297291964928349738324\right) a{\left(n + 16 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(308366033167335343024589591 n^{3} + 53451423098225195843564006946 n^{2} + 3088364396343971929791331665880 n + 59480438361170695482401948905191\right) a{\left(n + 59 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(321798990321296570989457245 n^{3} + 56685439453304505247133811846 n^{2} + 3328404740125417702521254681303 n + 65144601432550636410983759760558\right) a{\left(n + 60 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(734779451951671158462502711 n^{3} + 38943566039311203606629748688 n^{2} + 684571701262092416051473190213 n + 3991842464067579121380976005788\right) a{\left(n + 17 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(1323914521049525975575301776 n^{3} + 73186552150323394064638042536 n^{2} + 1341591440631128005949371084157 n + 8154677872705460715500480538267\right) a{\left(n + 18 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(2850804579972188471628361268 n^{3} + 163282344025250614817641847658 n^{2} + 3100098964418064054620681812003 n + 19504315574431749151704487557165\right) a{\left(n + 19 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(2896995017906206252299296130 n^{3} - 343489994778188390924917055143 n^{2} - 20842743707011922696952650931347 n - 260690145701652966744289054216488\right) a{\left(n + 25 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(4329844799808913868110813919 n^{3} + 738441026828569960674599833680 n^{2} + 41979137364502851011205672296905 n + 795472472997659804535821680900536\right) a{\left(n + 58 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(4634720109473806034009340901 n^{3} + 777635939857731159218565892246 n^{2} + 43491005947589960965171417896549 n + 810760481516315944253432866354856\right) a{\left(n + 57 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(7247222552349986565393207379 n^{3} + 425907696296638003908617213370 n^{2} + 8289247397838179760784439485765 n + 53383602737263776282398741764870\right) a{\left(n + 20 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(8391059088562891240578067378 n^{3} - 1438926022504876622086848190065 n^{2} - 79588934278930067710500139000516 n - 946673328685323797038307914260477\right) a{\left(n + 26 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(14396147713283826139341161425 n^{3} + 355164975376210731443618364690 n^{2} - 6654773891720125216311131463489 n - 164920939980837525701262372327562\right) a{\left(n + 24 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(20386015717506941494195943893 n^{3} + 3364911010609884252329570916114 n^{2} + 185130899517271376133090009151946 n + 3395064018388268246585527273566303\right) a{\left(n + 56 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(25548027755358540863740353904 n^{3} + 30632350149991244697236714896713 n^{2} + 2668914162965541949521288492733541 n + 60444034147871467449133358020088574\right) a{\left(n + 47 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(36014580661124589800962525421 n^{3} + 2135505473337184537684202691972 n^{2} + 41800562451407588407912604356201 n + 269523761251906121417922519191622\right) a{\left(n + 21 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(50224999938974819279694901351 n^{3} + 2899796741655322453795052153982 n^{2} + 54503587532967228937752645400535 n + 330374964640632256759724303901300\right) a{\left(n + 22 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(55641816030447403110488949887 n^{3} + 2824682219680220797548107746104 n^{2} + 42299754201850901494502363630785 n + 155925858945156047797507164749040\right) a{\left(n + 23 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(62104203543975898474319896889 n^{3} + 3719492780362250122879717528473 n^{2} + 88393315170398268641926708030654 n + 901210099294825100116143382340700\right) a{\left(n + 27 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(108880017037838702319257591251 n^{3} + 17680251003971652554340466308660 n^{2} + 956936190769700265399536282613551 n + 17263605623691015102097290386732826\right) a{\left(n + 55 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(222099592884156307950059573174 n^{3} + 20849135186919303578297853084621 n^{2} + 682317311976714212678342700552418 n + 7639112562063703014322498000510599\right) a{\left(n + 28 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(263739959886277599197756460383 n^{3} + 42138201095852442920367796668594 n^{2} + 2243958594696662432099854608398857 n + 39828354753999535428684329853640518\right) a{\left(n + 54 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(350820338698897698578619858897 n^{3} + 37204595640942033797343492272940 n^{2} + 1304870181779514657111689704947421 n + 15110842152671854703959737631749838\right) a{\left(n + 29 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(576099749615410279337146938047 n^{3} + 90594612252483662582073724070412 n^{2} + 4748108285335752100024294496599489 n + 82937882726481380501139933787332924\right) a{\left(n + 53 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(967009329807494484788734098632 n^{3} + 147716343814678957686242626654290 n^{2} + 7518246302934403874135424145236409 n + 127497305131387274479844691485160969\right) a{\left(n + 51 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(993291518049651190499950185929 n^{3} + 111981852967228710914183382420642 n^{2} + 4083822626987204407858106477998510 n + 48551268609525237187481960082564495\right) a{\left(n + 30 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(1124676906340852409846799017897 n^{3} + 174193739140460769367156501937538 n^{2} + 8990994243250990699702607823865597 n + 154651969115579282403641848955789424\right) a{\left(n + 52 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{2 \left(1498134425520806623942692242408 n^{3} + 190754735142566953406515426586688 n^{2} + 8070447366658427089220786269044286 n + 113408099027823923158830429613727955\right) a{\left(n + 45 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(1693273282488146319054361021681 n^{3} + 194742828021963580662532198872168 n^{2} + 7214393056239009200394846531661292 n + 86940661819627061422778664685429383\right) a{\left(n + 31 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(1736558236533300322927778936161 n^{3} + 213013909821337732816916685771250 n^{2} + 8600846348512538661647652260779719 n + 113919267840221666221089622060250374\right) a{\left(n + 46 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(2794640083020662502053649186467 n^{3} + 431755443411702099328252376474412 n^{2} + 22071850181903537786484656026532017 n + 373779468381958109167671761649545928\right) a{\left(n + 48 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(2853943166473652806517363765683 n^{3} + 431230696563459072684233974707660 n^{2} + 21701605218907632990464377294742711 n + 363756435557815005946448375718922842\right) a{\left(n + 50 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(3416547217004269004504632479853 n^{3} + 514482569148370300845314230026894 n^{2} + 25774717648103112599775764449670243 n + 429660974370990175391551354490956746\right) a{\left(n + 49 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(3593950091265193077871447568163 n^{3} + 367964668396402170998734453211536 n^{2} + 12497255759548666439219523279100059 n + 140696367706211029942956523943056896\right) a{\left(n + 36 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(4566248011347113045030597380118 n^{3} + 640947300901917041387126645919594 n^{2} + 29414368067877867570844245497059543 n + 443178931271932239967645734580987041\right) a{\left(n + 42 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(5158158439589133572206235453060 n^{3} + 552865493207060072519720946020883 n^{2} + 19533564499241082189950123692375948 n + 227901883063163517898258914578298957\right) a{\left(n + 33 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(5790414274788357193953122437789 n^{3} + 650315571601712340785094015226086 n^{2} + 23769630851858662875606148196428397 n + 284436629489472923024302278489334776\right) a{\left(n + 32 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(5808126714654278917915125500603 n^{3} + 743464736330267891717474950225600 n^{2} + 31658857924471665086864835774714353 n + 448416642880604417814531031406814132\right) a{\left(n + 44 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{2 \left(6672265421074648937015529965183 n^{3} + 691452982792260202804307258252835 n^{2} + 23761407133590144956945899759295383 n + 270533991558933880754631188503568964\right) a{\left(n + 37 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(7655203900115914646474527406491 n^{3} + 654035489295274408498844869645152 n^{2} + 15718316580422951030720245013669291 n + 72362110211188970718507473738396778\right) a{\left(n + 41 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(7741367317458531299878975848583 n^{3} + 821185529243180148928440866234199 n^{2} + 28825785349946662426546562419112258 n + 334355610615725356648283281482586268\right) a{\left(n + 39 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(9128227277755756279617237446687 n^{3} + 943664886752371318967427184696665 n^{2} + 32343473439809817787236236153011318 n + 367575849574598534736912347214920106\right) a{\left(n + 34 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(9962228114858019857160096239137 n^{3} + 1016244258621031413715236765457348 n^{2} + 34399395964690573942483605872776831 n + 386209068079626060782612349621732076\right) a{\left(n + 35 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(14254592339082593726737572569348 n^{3} + 1496069890184425565331595488533379 n^{2} + 51626652634338957367898284147785346 n + 583515182104364957842592016051354267\right) a{\left(n + 40 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(17522650379849377782719663197061 n^{3} + 2264764790771331297643937623723170 n^{2} + 97275816849931001827087852663488865 n + 1388607116148799458356123286527404344\right) a{\left(n + 43 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(55396553929878968116975389186283 n^{3} + 5821429037467354126693628757427830 n^{2} + 202749975263373010050086322325962557 n + 2337927639429702219452304518353140234\right) a{\left(n + 38 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)}, \quad n \geq 82
Specification 1
Strategy pack name: point_and_row_and_col_placements_req_corrob
Tree: http://www.permpal.com/tree/24767/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[134,x]+F[9,x]
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[4,x]
F[12,x] = F[13,x]+F[132,x]
F[13,x] = F[14,x]+F[9,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[4,x]
F[17,x] = 1/F[4,x]*F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[126,x]+F[20,x]
F[20,x] = F[116,x]+F[21,x]+F[28,x]
F[21,x] = F[22,x]*F[25,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[1,x]+F[22,x]
F[25,x] = F[1,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[25,x]*F[4,x]
F[28,x] = F[29,x]
F[29,x] = F[30,x]*F[4,x]
F[30,x] = F[115,x]+F[31,x]
F[31,x] = F[32,x]*F[46,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[24,x]+F[35,x]+F[43,x]
F[35,x] = F[36,x]
F[36,x] = F[34,x]*F[37,x]*F[4,x]
F[37,x] = F[1,x]+F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[1,x]+F[40,x]+F[42,x]
F[40,x] = F[41,x]
F[41,x] = F[37,x]*F[39,x]*F[4,x]
F[42,x] = F[39,x]*F[4,x]
F[43,x] = F[44,x]
F[44,x] = F[34,x]*F[4,x]*F[45,x]
F[45,x] = F[32,x]+F[37,x]
F[46,x] = F[47,x]+F[50,x]
F[47,x] = F[0,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[4,x]*F[46,x]
F[50,x] = F[51,x]+F[52,x]+F[54,x]
F[51,x] = 0
F[52,x] = F[53,x]
F[53,x] = F[37,x]*F[4,x]*F[46,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[113,x]+F[57,x]
F[57,x] = F[111,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]+F[62,x]+F[64,x]+F[80,x]
F[61,x] = F[25,x]^2
F[62,x] = F[63,x]
F[63,x] = F[25,x]*F[37,x]*F[4,x]*F[60,x]
F[64,x] = F[65,x]
F[65,x] = F[25,x]*F[4,x]*F[66,x]*F[77,x]
F[66,x] = 1/F[4,x]/F[77,x]*F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[69,x]+F[79,x]
F[69,x] = F[70,x]
F[70,x] = F[4,x]*F[71,x]*F[77,x]
F[71,x] = F[37,x]+F[72,x]
F[72,x] = F[51,x]+F[73,x]+F[75,x]
F[73,x] = F[74,x]
F[74,x] = F[37,x]*F[4,x]*F[71,x]
F[75,x] = F[76,x]
F[76,x] = F[37,x]*F[4,x]*F[72,x]
F[77,x] = 1/F[4,x]*F[78,x]
F[78,x] = F[48,x]
F[79,x] = F[4,x]*F[68,x]
F[80,x] = F[25,x]*F[4,x]*F[81,x]
F[81,x] = F[82,x]+F[88,x]
F[82,x] = F[58,x]+F[83,x]
F[83,x] = F[0,x]+F[84,x]
F[84,x] = F[85,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = 1/F[4,x]*F[87,x]
F[87,x] = F[6,x]
F[88,x] = F[89,x]
F[89,x] = F[25,x]*F[4,x]*F[90,x]
F[90,x] = F[82,x]+F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[37,x]*F[4,x]*F[93,x]
F[93,x] = F[61,x]+F[80,x]+F[94,x]+F[95,x]+F[99,x]
F[94,x] = F[92,x]
F[95,x] = F[96,x]
F[96,x] = F[4,x]*F[60,x]*F[97,x]
F[97,x] = F[72,x]+F[98,x]
F[98,x] = F[25,x]*F[37,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[4,x]*F[77,x]
F[101,x] = F[102,x]+F[103,x]
F[102,x] = F[25,x]*F[66,x]
F[103,x] = F[104,x]+F[107,x]+F[109,x]+F[51,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]*F[37,x]*F[4,x]
F[106,x] = F[103,x]+F[71,x]
F[107,x] = F[108,x]
F[108,x] = F[4,x]*F[71,x]*F[72,x]
F[109,x] = F[110,x]
F[110,x] = F[103,x]*F[37,x]*F[4,x]
F[111,x] = F[112,x]
F[112,x] = F[4,x]*F[72,x]*F[77,x]
F[113,x] = F[114,x]
F[114,x] = F[4,x]*F[91,x]
F[115,x] = F[20,x]*F[45,x]
F[116,x] = F[117,x]
F[117,x] = F[118,x]*F[22,x]*F[4,x]
F[118,x] = F[119,x]+F[125,x]
F[119,x] = 1/F[4,x]*F[120,x]
F[120,x] = F[121,x]
F[121,x] = F[122,x]+F[2,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[4,x]
F[124,x] = F[121,x]+F[50,x]
F[125,x] = F[113,x]+F[57,x]
F[126,x] = F[127,x]
F[127,x] = F[128,x]*F[32,x]*F[4,x]
F[128,x] = F[129,x]+F[130,x]
F[129,x] = F[15,x]+F[86,x]
F[130,x] = F[131,x]
F[131,x] = F[129,x]*F[39,x]*F[4,x]
F[132,x] = F[133,x]
F[133,x] = F[13,x]*F[39,x]*F[4,x]
F[134,x] = F[135,x]
F[135,x] = F[136,x]*F[4,x]
F[136,x] = F[137,x]+F[246,x]
F[137,x] = 1/F[4,x]*F[138,x]
F[138,x] = F[139,x]
F[139,x] = -F[243,x]+F[140,x]
F[140,x] = F[141,x]+F[158,x]+F[160,x]
F[141,x] = F[142,x]*F[24,x]
F[142,x] = F[143,x]+F[146,x]
F[143,x] = F[1,x]+F[144,x]
F[144,x] = F[145,x]
F[145,x] = F[142,x]*F[4,x]
F[146,x] = F[144,x]+F[147,x]
F[147,x] = F[148,x]+F[151,x]+F[51,x]
F[148,x] = F[149,x]*F[4,x]
F[149,x] = F[150,x]
F[150,x] = F[144,x]+F[147,x]
F[151,x] = F[152,x]*F[4,x]
F[152,x] = F[153,x]+F[154,x]
F[153,x] = F[26,x]
F[154,x] = F[155,x]
F[155,x] = F[151,x]+F[156,x]+F[51,x]
F[156,x] = F[157,x]*F[4,x]
F[157,x] = F[144,x]+F[155,x]
F[158,x] = F[159,x]
F[159,x] = F[140,x]*F[4,x]*F[45,x]
F[160,x] = F[161,x]*F[4,x]
F[161,x] = F[162,x]+F[216,x]+F[242,x]
F[162,x] = F[163,x]+F[194,x]
F[163,x] = F[164,x]+F[192,x]
F[164,x] = F[165,x]+F[190,x]+F[83,x]
F[165,x] = F[166,x]*F[4,x]
F[166,x] = 1/F[4,x]*F[167,x]
F[167,x] = -F[168,x]-F[184,x]+F[86,x]
F[168,x] = F[143,x]+F[169,x]
F[169,x] = F[170,x]
F[170,x] = F[171,x]*F[4,x]
F[171,x] = F[172,x]+F[183,x]
F[172,x] = F[173,x]*F[181,x]
F[173,x] = F[1,x]+F[174,x]
F[174,x] = F[175,x]
F[175,x] = F[176,x]*F[4,x]
F[176,x] = F[173,x]+F[177,x]
F[177,x] = F[178,x]+F[26,x]
F[178,x] = F[179,x]
F[179,x] = F[180,x]*F[4,x]
F[180,x] = F[174,x]+F[178,x]
F[181,x] = F[143,x]+F[182,x]
F[182,x] = F[155,x]+F[26,x]
F[183,x] = F[169,x]
F[184,x] = F[185,x]
F[185,x] = F[186,x]*F[4,x]
F[186,x] = F[187,x]+F[188,x]
F[187,x] = F[37,x]*F[86,x]
F[188,x] = F[189,x]
F[189,x] = F[128,x]*F[173,x]*F[4,x]*F[97,x]
F[190,x] = F[191,x]
F[191,x] = F[186,x]*F[4,x]
F[192,x] = F[193,x]
F[193,x] = F[128,x]*F[25,x]*F[37,x]*F[4,x]
F[194,x] = F[195,x]+F[198,x]+F[214,x]
F[195,x] = F[165,x]+F[196,x]+F[51,x]
F[196,x] = F[197,x]
F[197,x] = F[188,x]*F[4,x]
F[198,x] = F[199,x]
F[199,x] = F[200,x]*F[4,x]
F[200,x] = F[194,x]+F[201,x]
F[201,x] = F[202,x]
F[202,x] = F[203,x]*F[22,x]
F[203,x] = 1/F[24,x]/F[4,x]*F[204,x]
F[204,x] = F[205,x]
F[205,x] = -F[206,x]-F[207,x]-F[209,x]+F[17,x]
F[206,x] = F[181,x]*F[24,x]
F[207,x] = F[208,x]
F[208,x] = F[17,x]*F[37,x]*F[4,x]
F[209,x] = F[210,x]
F[210,x] = F[211,x]*F[34,x]*F[4,x]
F[211,x] = F[205,x]+F[206,x]+F[212,x]
F[212,x] = F[213,x]
F[213,x] = F[211,x]*F[4,x]*F[45,x]
F[214,x] = F[215,x]
F[215,x] = F[211,x]*F[32,x]*F[4,x]
F[216,x] = F[217,x]
F[217,x] = F[218,x]*F[4,x]
F[218,x] = 1/F[4,x]*F[219,x]
F[219,x] = F[220,x]
F[220,x] = F[221,x]*F[4,x]
F[221,x] = F[222,x]+F[237,x]
F[222,x] = F[223,x]+F[224,x]+F[226,x]+F[235,x]
F[223,x] = F[24,x]^2*F[181,x]
F[224,x] = F[225,x]
F[225,x] = F[222,x]*F[4,x]*F[45,x]
F[226,x] = F[227,x]
F[227,x] = F[211,x]*F[228,x]*F[4,x]
F[228,x] = F[229,x]+F[230,x]
F[229,x] = F[24,x]*F[45,x]
F[230,x] = F[231,x]+F[233,x]+F[51,x]
F[231,x] = F[232,x]
F[232,x] = F[228,x]*F[4,x]*F[45,x]
F[233,x] = F[234,x]
F[234,x] = F[230,x]*F[4,x]*F[45,x]
F[235,x] = F[236,x]
F[236,x] = F[24,x]^2*F[203,x]*F[4,x]
F[237,x] = F[238,x]
F[238,x] = F[222,x]*F[239,x]*F[4,x]
F[239,x] = F[240,x]+F[45,x]
F[240,x] = F[241,x]
F[241,x] = F[239,x]*F[4,x]*F[45,x]
F[242,x] = F[161,x]*F[4,x]
F[243,x] = F[244,x]+F[9,x]
F[244,x] = F[245,x]
F[245,x] = F[128,x]*F[37,x]*F[4,x]
F[246,x] = -F[247,x]+F[222,x]
F[247,x] = 1/F[4,x]*F[248,x]
F[248,x] = F[19,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{134}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{132}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{9}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{126}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{116}\! \left(x \right)+F_{21}\! \left(x \right)+F_{28}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{115}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{46}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{24}\! \left(x \right)+F_{35}\! \left(x \right)+F_{43}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{34}\! \left(x \right) F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{1}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{1}\! \left(x \right)+F_{40}\! \left(x \right)+F_{42}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{37}\! \left(x \right) F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{42}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{32}\! \left(x \right)+F_{37}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{50}\! \left(x \right)
F_{47}\! \left(x \right) = F_{0}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)+F_{54}\! \left(x \right)
F_{51}\! \left(x \right) = 0
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{113}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{111}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{62}\! \left(x \right)+F_{64}\! \left(x \right)+F_{80}\! \left(x \right)
F_{61}\! \left(x \right) = F_{25} \left(x \right)^{2}
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{25}\! \left(x \right) F_{37}\! \left(x \right) F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right) F_{66}\! \left(x \right) F_{77}\! \left(x \right)
F_{66}\! \left(x \right) = \frac{F_{67}\! \left(x \right)}{F_{4}\! \left(x \right) F_{77}\! \left(x \right)}
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{79}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right) F_{77}\! \left(x \right)
F_{71}\! \left(x \right) = F_{37}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{51}\! \left(x \right)+F_{73}\! \left(x \right)+F_{75}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{77}\! \left(x \right) = \frac{F_{78}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{78}\! \left(x \right) = F_{48}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{80}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{88}\! \left(x \right)
F_{82}\! \left(x \right) = F_{58}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{0}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = \frac{F_{87}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{87}\! \left(x \right) = F_{6}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{82}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{61}\! \left(x \right)+F_{80}\! \left(x \right)+F_{94}\! \left(x \right)+F_{95}\! \left(x \right)+F_{99}\! \left(x \right)
F_{94}\! \left(x \right) = F_{92}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{72}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{25}\! \left(x \right) F_{37}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{103}\! \left(x \right)
F_{102}\! \left(x \right) = F_{25}\! \left(x \right) F_{66}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{107}\! \left(x \right)+F_{109}\! \left(x \right)+F_{51}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{106}\! \left(x \right) = F_{103}\! \left(x \right)+F_{71}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right) F_{72}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{103}\! \left(x \right) F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right) F_{77}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{115}\! \left(x \right) = F_{20}\! \left(x \right) F_{45}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{125}\! \left(x \right)
F_{119}\! \left(x \right) = \frac{F_{120}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{2}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{4}\! \left(x \right)
F_{124}\! \left(x \right) = F_{121}\! \left(x \right)+F_{50}\! \left(x \right)
F_{125}\! \left(x \right) = F_{113}\! \left(x \right)+F_{57}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{130}\! \left(x \right)
F_{129}\! \left(x \right) = F_{15}\! \left(x \right)+F_{86}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{129}\! \left(x \right) F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{13}\! \left(x \right) F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{4}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{246}\! \left(x \right)
F_{137}\! \left(x \right) = \frac{F_{138}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = -F_{243}\! \left(x \right)+F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{158}\! \left(x \right)+F_{160}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right) F_{24}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{146}\! \left(x \right)
F_{143}\! \left(x \right) = F_{1}\! \left(x \right)+F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{142}\! \left(x \right) F_{4}\! \left(x \right)
F_{146}\! \left(x \right) = F_{144}\! \left(x \right)+F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{151}\! \left(x \right)+F_{51}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right) F_{4}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{144}\! \left(x \right)+F_{147}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{4}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{154}\! \left(x \right)
F_{153}\! \left(x \right) = F_{26}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{151}\! \left(x \right)+F_{156}\! \left(x \right)+F_{51}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right) F_{4}\! \left(x \right)
F_{157}\! \left(x \right) = F_{144}\! \left(x \right)+F_{155}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{140}\! \left(x \right) F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right) F_{4}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{216}\! \left(x \right)+F_{242}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)+F_{194}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)+F_{192}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)+F_{190}\! \left(x \right)+F_{83}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right) F_{4}\! \left(x \right)
F_{166}\! \left(x \right) = \frac{F_{167}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{167}\! \left(x \right) = -F_{168}\! \left(x \right)-F_{184}\! \left(x \right)+F_{86}\! \left(x \right)
F_{168}\! \left(x \right) = F_{143}\! \left(x \right)+F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right) F_{4}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{183}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right) F_{181}\! \left(x \right)
F_{173}\! \left(x \right) = F_{1}\! \left(x \right)+F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right) F_{4}\! \left(x \right)
F_{176}\! \left(x \right) = F_{173}\! \left(x \right)+F_{177}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)+F_{26}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right) F_{4}\! \left(x \right)
F_{180}\! \left(x \right) = F_{174}\! \left(x \right)+F_{178}\! \left(x \right)
F_{181}\! \left(x \right) = F_{143}\! \left(x \right)+F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{155}\! \left(x \right)+F_{26}\! \left(x \right)
F_{183}\! \left(x \right) = F_{169}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right) F_{4}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)+F_{188}\! \left(x \right)
F_{187}\! \left(x \right) = F_{37}\! \left(x \right) F_{86}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{128}\! \left(x \right) F_{173}\! \left(x \right) F_{4}\! \left(x \right) F_{97}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{186}\! \left(x \right) F_{4}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)
F_{193}\! \left(x \right) = F_{128}\! \left(x \right) F_{25}\! \left(x \right) F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)+F_{198}\! \left(x \right)+F_{214}\! \left(x \right)
F_{195}\! \left(x \right) = F_{165}\! \left(x \right)+F_{196}\! \left(x \right)+F_{51}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right)
F_{197}\! \left(x \right) = F_{188}\! \left(x \right) F_{4}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right) F_{4}\! \left(x \right)
F_{200}\! \left(x \right) = F_{194}\! \left(x \right)+F_{201}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right) F_{22}\! \left(x \right)
F_{203}\! \left(x \right) = \frac{F_{204}\! \left(x \right)}{F_{24}\! \left(x \right) F_{4}\! \left(x \right)}
F_{204}\! \left(x \right) = F_{205}\! \left(x \right)
F_{205}\! \left(x \right) = -F_{206}\! \left(x \right)-F_{207}\! \left(x \right)-F_{209}\! \left(x \right)+F_{17}\! \left(x \right)
F_{206}\! \left(x \right) = F_{181}\! \left(x \right) F_{24}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)
F_{208}\! \left(x \right) = F_{17}\! \left(x \right) F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{209}\! \left(x \right) = F_{210}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right) F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{211}\! \left(x \right) = F_{205}\! \left(x \right)+F_{206}\! \left(x \right)+F_{212}\! \left(x \right)
F_{212}\! \left(x \right) = F_{213}\! \left(x \right)
F_{213}\! \left(x \right) = F_{211}\! \left(x \right) F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{214}\! \left(x \right) = F_{215}\! \left(x \right)
F_{215}\! \left(x \right) = F_{211}\! \left(x \right) F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{216}\! \left(x \right) = F_{217}\! \left(x \right)
F_{217}\! \left(x \right) = F_{218}\! \left(x \right) F_{4}\! \left(x \right)
F_{218}\! \left(x \right) = \frac{F_{219}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{219}\! \left(x \right) = F_{220}\! \left(x \right)
F_{220}\! \left(x \right) = F_{221}\! \left(x \right) F_{4}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x \right)+F_{237}\! \left(x \right)
F_{222}\! \left(x \right) = F_{223}\! \left(x \right)+F_{224}\! \left(x \right)+F_{226}\! \left(x \right)+F_{235}\! \left(x \right)
F_{223}\! \left(x \right) = F_{24} \left(x \right)^{2} F_{181}\! \left(x \right)
F_{224}\! \left(x \right) = F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = F_{222}\! \left(x \right) F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{226}\! \left(x \right) = F_{227}\! \left(x \right)
F_{227}\! \left(x \right) = F_{211}\! \left(x \right) F_{228}\! \left(x \right) F_{4}\! \left(x \right)
F_{228}\! \left(x \right) = F_{229}\! \left(x \right)+F_{230}\! \left(x \right)
F_{229}\! \left(x \right) = F_{24}\! \left(x \right) F_{45}\! \left(x \right)
F_{230}\! \left(x \right) = F_{231}\! \left(x \right)+F_{233}\! \left(x \right)+F_{51}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x \right)
F_{232}\! \left(x \right) = F_{228}\! \left(x \right) F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{233}\! \left(x \right) = F_{234}\! \left(x \right)
F_{234}\! \left(x \right) = F_{230}\! \left(x \right) F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{235}\! \left(x \right) = F_{236}\! \left(x \right)
F_{236}\! \left(x \right) = F_{24} \left(x \right)^{2} F_{203}\! \left(x \right) F_{4}\! \left(x \right)
F_{237}\! \left(x \right) = F_{238}\! \left(x \right)
F_{238}\! \left(x \right) = F_{222}\! \left(x \right) F_{239}\! \left(x \right) F_{4}\! \left(x \right)
F_{239}\! \left(x \right) = F_{240}\! \left(x \right)+F_{45}\! \left(x \right)
F_{240}\! \left(x \right) = F_{241}\! \left(x \right)
F_{241}\! \left(x \right) = F_{239}\! \left(x \right) F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{242}\! \left(x \right) = F_{161}\! \left(x \right) F_{4}\! \left(x \right)
F_{243}\! \left(x \right) = F_{244}\! \left(x \right)+F_{9}\! \left(x \right)
F_{244}\! \left(x \right) = F_{245}\! \left(x \right)
F_{245}\! \left(x \right) = F_{128}\! \left(x \right) F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{246}\! \left(x \right) = -F_{247}\! \left(x \right)+F_{222}\! \left(x \right)
F_{247}\! \left(x \right) = \frac{F_{248}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{248}\! \left(x \right) = F_{19}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_134(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_4(x))
Eq(F_12(x), F_13(x) + F_132(x))
Eq(F_13(x), F_14(x) + F_9(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_18(x)/F_4(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_126(x) + F_20(x))
Eq(F_20(x), F_116(x) + F_21(x) + F_28(x))
Eq(F_21(x), F_22(x)*F_25(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_1(x) + F_22(x))
Eq(F_25(x), F_1(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_25(x)*F_4(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x)*F_4(x))
Eq(F_30(x), F_115(x) + F_31(x))
Eq(F_31(x), F_32(x)*F_46(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_24(x) + F_35(x) + F_43(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_34(x)*F_37(x)*F_4(x))
Eq(F_37(x), F_1(x) + F_38(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_1(x) + F_40(x) + F_42(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_37(x)*F_39(x)*F_4(x))
Eq(F_42(x), F_39(x)*F_4(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_34(x)*F_4(x)*F_45(x))
Eq(F_45(x), F_32(x) + F_37(x))
Eq(F_46(x), F_47(x) + F_50(x))
Eq(F_47(x), F_0(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_4(x)*F_46(x))
Eq(F_50(x), F_51(x) + F_52(x) + F_54(x))
Eq(F_51(x), 0)
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_37(x)*F_4(x)*F_46(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_113(x) + F_57(x))
Eq(F_57(x), F_111(x) + F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_62(x) + F_64(x) + F_80(x))
Eq(F_61(x), F_25(x)**2)
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_25(x)*F_37(x)*F_4(x)*F_60(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_25(x)*F_4(x)*F_66(x)*F_77(x))
Eq(F_66(x), F_67(x)/(F_4(x)*F_77(x)))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_69(x) + F_79(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_4(x)*F_71(x)*F_77(x))
Eq(F_71(x), F_37(x) + F_72(x))
Eq(F_72(x), F_51(x) + F_73(x) + F_75(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_37(x)*F_4(x)*F_71(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_37(x)*F_4(x)*F_72(x))
Eq(F_77(x), F_78(x)/F_4(x))
Eq(F_78(x), F_48(x))
Eq(F_79(x), F_4(x)*F_68(x))
Eq(F_80(x), F_25(x)*F_4(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_88(x))
Eq(F_82(x), F_58(x) + F_83(x))
Eq(F_83(x), F_0(x) + F_84(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_87(x)/F_4(x))
Eq(F_87(x), F_6(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_25(x)*F_4(x)*F_90(x))
Eq(F_90(x), F_82(x) + F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_37(x)*F_4(x)*F_93(x))
Eq(F_93(x), F_61(x) + F_80(x) + F_94(x) + F_95(x) + F_99(x))
Eq(F_94(x), F_92(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_4(x)*F_60(x)*F_97(x))
Eq(F_97(x), F_72(x) + F_98(x))
Eq(F_98(x), F_25(x)*F_37(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_4(x)*F_77(x))
Eq(F_101(x), F_102(x) + F_103(x))
Eq(F_102(x), F_25(x)*F_66(x))
Eq(F_103(x), F_104(x) + F_107(x) + F_109(x) + F_51(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x)*F_37(x)*F_4(x))
Eq(F_106(x), F_103(x) + F_71(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_4(x)*F_71(x)*F_72(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_103(x)*F_37(x)*F_4(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_4(x)*F_72(x)*F_77(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_4(x)*F_91(x))
Eq(F_115(x), F_20(x)*F_45(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_118(x)*F_22(x)*F_4(x))
Eq(F_118(x), F_119(x) + F_125(x))
Eq(F_119(x), F_120(x)/F_4(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_122(x) + F_2(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_4(x))
Eq(F_124(x), F_121(x) + F_50(x))
Eq(F_125(x), F_113(x) + F_57(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_128(x)*F_32(x)*F_4(x))
Eq(F_128(x), F_129(x) + F_130(x))
Eq(F_129(x), F_15(x) + F_86(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_129(x)*F_39(x)*F_4(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_13(x)*F_39(x)*F_4(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_136(x)*F_4(x))
Eq(F_136(x), F_137(x) + F_246(x))
Eq(F_137(x), F_138(x)/F_4(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_140(x) - F_243(x))
Eq(F_140(x), F_141(x) + F_158(x) + F_160(x))
Eq(F_141(x), F_142(x)*F_24(x))
Eq(F_142(x), F_143(x) + F_146(x))
Eq(F_143(x), F_1(x) + F_144(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_142(x)*F_4(x))
Eq(F_146(x), F_144(x) + F_147(x))
Eq(F_147(x), F_148(x) + F_151(x) + F_51(x))
Eq(F_148(x), F_149(x)*F_4(x))
Eq(F_149(x), F_150(x))
Eq(F_150(x), F_144(x) + F_147(x))
Eq(F_151(x), F_152(x)*F_4(x))
Eq(F_152(x), F_153(x) + F_154(x))
Eq(F_153(x), F_26(x))
Eq(F_154(x), F_155(x))
Eq(F_155(x), F_151(x) + F_156(x) + F_51(x))
Eq(F_156(x), F_157(x)*F_4(x))
Eq(F_157(x), F_144(x) + F_155(x))
Eq(F_158(x), F_159(x))
Eq(F_159(x), F_140(x)*F_4(x)*F_45(x))
Eq(F_160(x), F_161(x)*F_4(x))
Eq(F_161(x), F_162(x) + F_216(x) + F_242(x))
Eq(F_162(x), F_163(x) + F_194(x))
Eq(F_163(x), F_164(x) + F_192(x))
Eq(F_164(x), F_165(x) + F_190(x) + F_83(x))
Eq(F_165(x), F_166(x)*F_4(x))
Eq(F_166(x), F_167(x)/F_4(x))
Eq(F_167(x), -F_168(x) - F_184(x) + F_86(x))
Eq(F_168(x), F_143(x) + F_169(x))
Eq(F_169(x), F_170(x))
Eq(F_170(x), F_171(x)*F_4(x))
Eq(F_171(x), F_172(x) + F_183(x))
Eq(F_172(x), F_173(x)*F_181(x))
Eq(F_173(x), F_1(x) + F_174(x))
Eq(F_174(x), F_175(x))
Eq(F_175(x), F_176(x)*F_4(x))
Eq(F_176(x), F_173(x) + F_177(x))
Eq(F_177(x), F_178(x) + F_26(x))
Eq(F_178(x), F_179(x))
Eq(F_179(x), F_180(x)*F_4(x))
Eq(F_180(x), F_174(x) + F_178(x))
Eq(F_181(x), F_143(x) + F_182(x))
Eq(F_182(x), F_155(x) + F_26(x))
Eq(F_183(x), F_169(x))
Eq(F_184(x), F_185(x))
Eq(F_185(x), F_186(x)*F_4(x))
Eq(F_186(x), F_187(x) + F_188(x))
Eq(F_187(x), F_37(x)*F_86(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_128(x)*F_173(x)*F_4(x)*F_97(x))
Eq(F_190(x), F_191(x))
Eq(F_191(x), F_186(x)*F_4(x))
Eq(F_192(x), F_193(x))
Eq(F_193(x), F_128(x)*F_25(x)*F_37(x)*F_4(x))
Eq(F_194(x), F_195(x) + F_198(x) + F_214(x))
Eq(F_195(x), F_165(x) + F_196(x) + F_51(x))
Eq(F_196(x), F_197(x))
Eq(F_197(x), F_188(x)*F_4(x))
Eq(F_198(x), F_199(x))
Eq(F_199(x), F_200(x)*F_4(x))
Eq(F_200(x), F_194(x) + F_201(x))
Eq(F_201(x), F_202(x))
Eq(F_202(x), F_203(x)*F_22(x))
Eq(F_203(x), F_204(x)/(F_24(x)*F_4(x)))
Eq(F_204(x), F_205(x))
Eq(F_205(x), F_17(x) - F_206(x) - F_207(x) - F_209(x))
Eq(F_206(x), F_181(x)*F_24(x))
Eq(F_207(x), F_208(x))
Eq(F_208(x), F_17(x)*F_37(x)*F_4(x))
Eq(F_209(x), F_210(x))
Eq(F_210(x), F_211(x)*F_34(x)*F_4(x))
Eq(F_211(x), F_205(x) + F_206(x) + F_212(x))
Eq(F_212(x), F_213(x))
Eq(F_213(x), F_211(x)*F_4(x)*F_45(x))
Eq(F_214(x), F_215(x))
Eq(F_215(x), F_211(x)*F_32(x)*F_4(x))
Eq(F_216(x), F_217(x))
Eq(F_217(x), F_218(x)*F_4(x))
Eq(F_218(x), F_219(x)/F_4(x))
Eq(F_219(x), F_220(x))
Eq(F_220(x), F_221(x)*F_4(x))
Eq(F_221(x), F_222(x) + F_237(x))
Eq(F_222(x), F_223(x) + F_224(x) + F_226(x) + F_235(x))
Eq(F_223(x), F_181(x)*F_24(x)**2)
Eq(F_224(x), F_225(x))
Eq(F_225(x), F_222(x)*F_4(x)*F_45(x))
Eq(F_226(x), F_227(x))
Eq(F_227(x), F_211(x)*F_228(x)*F_4(x))
Eq(F_228(x), F_229(x) + F_230(x))
Eq(F_229(x), F_24(x)*F_45(x))
Eq(F_230(x), F_231(x) + F_233(x) + F_51(x))
Eq(F_231(x), F_232(x))
Eq(F_232(x), F_228(x)*F_4(x)*F_45(x))
Eq(F_233(x), F_234(x))
Eq(F_234(x), F_230(x)*F_4(x)*F_45(x))
Eq(F_235(x), F_236(x))
Eq(F_236(x), F_203(x)*F_24(x)**2*F_4(x))
Eq(F_237(x), F_238(x))
Eq(F_238(x), F_222(x)*F_239(x)*F_4(x))
Eq(F_239(x), F_240(x) + F_45(x))
Eq(F_240(x), F_241(x))
Eq(F_241(x), F_239(x)*F_4(x)*F_45(x))
Eq(F_242(x), F_161(x)*F_4(x))
Eq(F_243(x), F_244(x) + F_9(x))
Eq(F_244(x), F_245(x))
Eq(F_245(x), F_128(x)*F_37(x)*F_4(x))
Eq(F_246(x), F_222(x) - F_247(x))
Eq(F_247(x), F_248(x)/F_4(x))
Eq(F_248(x), F_19(x))
Pack JSON:
{"name": "point_and_row_and_col_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 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